Quince clan: Difference between revisions
deleted counterbenediction, counterrevelation. canonicalized countermiraculous |
Partial revert. + explanations |
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Like miracle, it is naturally an 11-limit temperament with the generator representing [[77/72]], but here the generator does not represent [[15/14]] or [[16/15]]. | Like miracle, it is naturally an 11-limit temperament with the generator representing [[77/72]], but here the generator does not represent [[15/14]] or [[16/15]]. | ||
Countermiracle extends less naturally to the 13- and 17-limit, with countermiraculous (31 & 145), countermanna (145 & 176), and counterbenediction (176 & 207) being possible candidates, each favoring a tuning range shown by the [[temperament merging|equal-temperament joins]]. | |||
[[Subgroup]]: 2.3.5.7 | [[Subgroup]]: 2.3.5.7 | ||
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Badness (Sintel): 1.29 | Badness (Sintel): 1.29 | ||
=== | ==== Countermiraculous ==== | ||
Subgroup: 2.3.5.7.11.13 | Subgroup: 2.3.5.7.11.13 | ||
| Line 90: | Line 90: | ||
Badness (Sintel): 1.62 | Badness (Sintel): 1.62 | ||
=== 17-limit === | ===== 17-limit ===== | ||
Subgroup: 2.3.5.7.11.13.17 | Subgroup: 2.3.5.7.11.13.17 | ||
| Line 104: | Line 104: | ||
Badness (Sintel): 1.50 | Badness (Sintel): 1.50 | ||
==== Counterbenediction ==== | |||
Subgroup: 2.3.5.7.11.13 | |||
Comma list: 351/350, 441/440, 3146/3125, 3584/3575 | |||
Mapping: {{mapping| 1 -21 -4 1 -39 29 57 | 0 25 7 2 47 -59 }} | |||
Optimal tunings: | |||
* WE: ~2 = 1199.9460{{c}}, ~144/77 = 1084.0178{{c}} (~77/72 = 115.9283{{c}}) | |||
* CWE: ~2 = 1200.0000{{c}}, ~144/77 = 1084.0663{{c}} (~77/72 = 115.9337{{c}}) | |||
{{Optimal ET sequence|legend=0| 31, 145f, 176, 207 }} | |||
Badness (Sintel): 1.88 | |||
===== 17-limit ===== | |||
Subgroup: 2.3.5.7.11.13.17 | |||
Comma list: 351/350, 441/440, 561/560, 1632/1625, 3146/3125 | |||
Mapping: {{mapping| 1 -21 -4 1 -39 29 57 61 | 0 25 7 2 47 -59 -63 }} | |||
Optimal tunings: | |||
* WE: ~2 = 1199.9950{{c}}, ~144/77 = 1084.0564{{c}} (~77/72 = 115.9386{{c}}) | |||
* CWE: ~2 = 1200.0000{{c}}, ~144/77 = 1084.0609{{c}} (~77/72 = 115.9391{{c}}) | |||
{{Optimal ET sequence|legend=0| 31, 176, 207 }} | |||
Badness (Sintel): 1.85 | |||
==== Countermanna ==== | |||
Subgroup: 2.3.5.7.11.13 | |||
Comma list: 364/363, 441/440, 3388/3375, 6144/6125 | |||
Mapping: {{mapping| 1 -21 -4 1 -39 -102 | 0 25 7 2 47 117 }} | |||
Optimal tunings: | |||
* WE: ~2 = 1199.6687{{c}}, ~144/77 = 1083.8108{{c}} (~77/72 = 115.8578{{c}}) | |||
* CWE: ~2 = 1200.0000{{c}}, ~144/77 = 1084.1065{{c}} (~77/72 = 115.8935{{c}}) | |||
{{Optimal ET sequence|legend=0| 31f, 145, 176, 321ce }} | |||
Badness (Sintel): 2.21 | |||
===== 17-limit ===== | |||
Subgroup: 2.3.5.7.11.13.17 | |||
Comma list: 364/363, 441/440, 595/594, 1632/1625, 3388/3375 | |||
Mapping: {{mapping| 1 -21 -4 1 -39 -102 -98 | 0 25 7 2 47 117 113 }} | |||
Optimal tunings: | |||
* WE: ~2 = 1199.6458{{c}}, ~144/77 = 1083.7968{{c}} (~77/72 = 115.8490{{c}}) | |||
* CWE: ~2 = 1200.0000{{c}}, ~144/77 = 1084.1132{{c}} (~77/72 = 115.8868{{c}}) | |||
{{Optimal ET sequence|legend=0| 31fg, 145, 321ce }} | |||
Badness (Sintel): 2.08 | |||
== Subgroup extensions == | == Subgroup extensions == | ||